Liz, I find it very easy to believe that a fierce cat would see off a fox. A cat's body is designed as a fighting machine, which is the envy of every martial arts master in the world! They have astonishing agility, speed, balance and acceleration.
What I find less easy to believe is that rabbits make easy dinners for foxes. I once watched a fox pursue three different rabbits, one after the other. They all evaded him with near contemptuous ease. Rabbits just move too fast over a short distance. Of course, if the fox can get his jaws on one, it's rabbit pie. The rabbit would have to make a very stupid mistake for that to happen. The studies I have read conclude that it happens, but it is rare.